# A machine costs Rs. 80,000 and the operating cost is estimated to be Rs. 5000 for the first year and increases by

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A machine costs Rs. 80,000 and the operating cost is estimated to be Rs. 5000 for the first year and increases by Rs. 7000 every year for next five years. Determine the optimum period for replacement of the machine, assuming that the machine has no scrap (Resale) value.

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Here the machine cost = P = Rs. 80,000 and since resale value Sn = 0 ; the depreciation (P – Sn) = 80000 for all the years and let Ci be the operating cost. The Average annual cost A(n) = $\frac{T}{n}$; Where T = Total cost = (P – Sn) + ΣCi and n = no. of years.

Here, Average annual cost A(n) is minimum for n = 5.

∴ The optimum replacement age is 5 years,

i.e., the machines should be replaced at the end of 5 years.

Minimum annual average cost = Rs. 35000

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